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<p>This study investigates the nonlinear vibrations of a parametrically excited active-magnetic-bearing (AMB) asymmetrical rotor system. A comprehensive mathematical model is developed for 8- and 16-pole AMBs functioning as actuators or supports, incorporating time-varying proportional-derivative (PD) controllers to characterize electromagnetic forces accurately. Using the variational approach and dimensionless parameters, partial differential equations of motion are derived and reduced to ordinary differential equations via the Galerkin method. The system exhibits complex dynamics, including primary, parametric, and combination resonances. The time-varying proportional controller enhances system controllability by exciting backward modes, significantly reducing vibration amplitudes in symmetrical and asymmetrical systems. This effect is amplified with an increased number of pole legs. Additionally, derivative gain impacts the system differently depending on support types: its influence is reduced in systems with journal bearings due to the combined effects of oil-film and magnetic forces, while systems with hinged-hinged supports display predominantly magnetic-driven behavior. The system demonstrates hardening behavior with journal bearings and softening behavior with simply-supported ends. Asymmetrical systems exhibit greater amplitude reductions than symmetrical ones, and system stability, bifurcation loci, and solution multiplicity are highly sensitive to variations in the air gap and coil current. Notably, the AMB actuator's position strongly affects peak vibration amplitudes, with the lowest peaks observed when the actuator is located at the shaft's midpoint. Shaft and disk eccentricities significantly influence nonlinear dynamics and bifurcation loci. Systems without shaft eccentricities exhibit lower vibration amplitudes and more stable solutions, with some approaching trivial responses. Analytical solutions derived via the multiple scales method, validated through numerical simulations, confirm that the time-varying controller effectively suppresses vibrations, highlighting its practical utility for vibration control in AMB-rotor systems.</p>

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Vibration control of a parametrically excited asymmetrical rotor-active magnetic bearings system with oil-film effect

  • 期刊论文

  • 发表日期：

    2025年4月16日

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  • Majid Shahgholi,
  • Jan Awrejcewicz

摘要

This study investigates the nonlinear vibrations of a parametrically excited active-magnetic-bearing (AMB) asymmetrical rotor system. A comprehensive mathematical model is developed for 8- and 16-pole AMBs functioning as actuators or supports, incorporating time-varying proportional-derivative (PD) controllers to characterize electromagnetic forces accurately. Using the variational approach and dimensionless parameters, partial differential equations of motion are derived and reduced to ordinary differential equations via the Galerkin method. The system exhibits complex dynamics, including primary, parametric, and combination resonances. The time-varying proportional controller enhances system controllability by exciting backward modes, significantly reducing vibration amplitudes in symmetrical and asymmetrical systems. This effect is amplified with an increased number of pole legs. Additionally, derivative gain impacts the system differently depending on support types: its influence is reduced in systems with journal bearings due to the combined effects of oil-film and magnetic forces, while systems with hinged-hinged supports display predominantly magnetic-driven behavior. The system demonstrates hardening behavior with journal bearings and softening behavior with simply-supported ends. Asymmetrical systems exhibit greater amplitude reductions than symmetrical ones, and system stability, bifurcation loci, and solution multiplicity are highly sensitive to variations in the air gap and coil current. Notably, the AMB actuator's position strongly affects peak vibration amplitudes, with the lowest peaks observed when the actuator is located at the shaft's midpoint. Shaft and disk eccentricities significantly influence nonlinear dynamics and bifurcation loci. Systems without shaft eccentricities exhibit lower vibration amplitudes and more stable solutions, with some approaching trivial responses. Analytical solutions derived via the multiple scales method, validated through numerical simulations, confirm that the time-varying controller effectively suppresses vibrations, highlighting its practical utility for vibration control in AMB-rotor systems.